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Enter your answer as a decimal in the box.

1) The interest if it is compounded using simple interest is $240

2) The interest if it is compounded annually is $249.73

3) The interest if it is compounded semiannually is $252.325

4) The interest if it is compounded quarterly is $253.650

5) The interest if it is compounded monthly is $254.543

6) The interest if it is compounded daily is $254.978

7) The interest if it is compounded hourly is $254.993

8) The interest if it is compounded every minute is $254.993

9) The interest if it is compounded continuously is $254.993

10) The difference in interest between simple interest and interest compounded continuously is $14.993

Compound interest is the addition of interest to the principal sum of a loan or deposit, or interest on interest plus interest.

Given, P=2000

r=4%

r=4/100

r=0.04

t=3 years

1) Simple interest⇒ A=P(1+rt)

=2000(1+3(0.04)

=2000(1+0.12)

=2240

S.I= 2240-2000

S.I=$240

2) Compound interest(yearly)

1st year= 2000(4/100)=80

2nd year=2080(4/100)=83.2

3rd year=(2080+83.2)(4/100)=86.528

P=2163.2+86.528

P=2249.728

C.I=2249.728-2000

C.I=249.728≈$249.73

3) Compounded semiannually

A= P(1+(R/200))²ⁿ

A=2000(1+(4/200))⁶

A=2000(1.12616)

A=2252.325

C.I= 2252.325-2000

C.I=$252.325

4) Compounded quarterly

A=P(1+(R/400))⁴ⁿ

A=2000(1+(4/400))¹²

A=2253.650

C.I=2253.650-2000

C.I=$253.650

5) Compounded monthly

A=P(1+(R/1200))³⁶

A=2000(1+(4/1200))³⁶

A=2254.543

C.I= 2254.543-2000

C.I=$254.543

6) Compounded daily

A=P(1+(R/36500))³⁶⁵ⁿ

A=2000(1+(4/36500))¹⁰⁹⁵

A=2254.978

C.I=2254.978-2000

C.I=$254.978

7) Compounded hourly

A=P(1+(R/876000))²⁶²⁸⁰

A=P(1+(4/876000))²⁶²⁸⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

8) Compounded every minute

A=P(1+(R/52560000))¹⁵⁷⁶⁸⁰⁰

A=P(1+(4/52560000))¹⁵⁷⁶⁸⁰⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

9) Compounded continuously

A= \(Pe^{rt}\)

A=2000(\(e^{0.04*3}\))

A=2254.993

C.I=2254.993-2000

C.I=$254.993

10) The difference in interest between simple interest and interest compounded continuously is

254.993-$240=$14.993

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Answer:

Answer First choice NO

Step-by-step explanation:

Direct Relationship

Two variables x and y have a direct relationship if the function that relates them is written as:

y = kx

Where k is the constant of proportionality.

The graph of such function is a straight line passing through the origin (0,0).

The graph does not show a direct relationship because it has the shape of a curve, not a straight line.

Answer First choice NO

Answer:

x = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

0.4(12 - 3x) = 0.3(12x - 16)

Step 2: Solve for x

Answer:

a) (1,4), b) -1 and 3, c) 3

Step-by-step explanation:

a) coordinates of turning point are the peak of the graph. this occurs at (1,4),

b) f(x) = 0 means where the graph meets x-axis. it meets x-axis at x = -1 and x =3,

c) f(0) means where the graph crosses the y-axis. it crosses at y = 3

Answer:

  71

Step-by-step explanation:

The congruency statement tells you ...

  KL = NO

  5x -3 = 4x +7

  x = 10 . . . . . . . . add 3-4x to both sides

Then that longest side is ...

  4(10)+7 = 47

Corresponding sides are the same length in both triangles. The perimeter is the sum of side lengths:

  P = 14 + 10 + 47 = 71

The perimeter of ΔKLM is 71 units.

_____

Additional comment

A triangle with these side lengths cannot exist. The short sides are too short to connect to the ends of the long side. (The long side must be between 14 and 24 units.) I suggest you talk to your teacher about this problem.

Step-by-step explanation:

r =6

sector =45°

R=6×45÷360

=0.75cm

Answer:

the sector bounded by 45 degrees arc is 70.56

I think

The median would be 22:

Step-by-step explanation: The median is the number that is in the middle

Simply defined, the median is the number right in the middle of a set.

But before I get down to finding the median, I will order the numbers from least to greatest:

15, 17, 19, 20, 21, 22, 23

Now, the middle number is 20. So that's the median.

As for the range, it's the difference between the largest number and the smallest one:

Range = Greatest number - Smallest number

           = 23 - 15

           = 6

In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.

x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √\((b^2 - 4ac)\)) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √\((144 - 160)\)) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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The equation that represents the relationship on the graph attached below is: y = 4/5x + 3.

Given a linear graph like the one attached below, showing the relationship between x and y, the equation that represents the relationship between x and y in the given graph can be expressed as: y = mx + b, where m is the slope (m) and b is the y-intercept (b) of the graph.

In the given image, the line intercepts the y-axis at 3, therefore the y-intercept of the graph is b = 3.

The slope of the graph (m) = change in y / change in x = (11 - 7)/(10 - 5)

m = 4/5

To write the equation of the relationship, substitute m = 4/5 and b = 3 into y = mx + b:

y = 4/5x + 3

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The general equation of a line with slope m and y-intercept b is:

Where the slope m of a line that passes thorugh two points (x_1,y_1) and (x_2,y_2) is given by:

Use the coordinates of the points (0,6) and (1,8) to find the slope of the desired line:

The y-intercept is the value at which the line crosses the y-axis when x=0. Since the point (0,6) is already being considered, we know that b=6.

Substitute m=2 and b=6 into the equation of a line in slope-intercept form:

Therefore, y=2x+8 is the equation of a line containing (0,6) and (1,8).

The fourth one 12.5!

It's self-explanatory, hope this helps!

Answer: x = -1

Step-by-step explanation:

simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there

Answer:

To divide exponents (or powers) with the same base, subtract the exponents. Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.Quotient Rule: , this says that to divide two exponents with the same base, you keep the base and subtract the powers. This is similar to reducing fractions; when you subtract the powers put the answer in the numerator or denominator depending on where the higher power was located.

Final answer

Subtraction

Answer:

0.49x + 0.34y = 6

Explanation:

Let us call x the pounds of bananas and y the pounds of apples.

Since one pound of bananas cost $0.49, the price of x pounds is

0.49x

Since one pound of apples cost $0.34

Answer:

Multiplicative

Step-by-step explanation:

If the area of the first rectangle is l*w, the area of the second would be 2w*w. The area is multiplied by 2 and the relationship is therefore multiplicative.

Answer: the total  price change in stock is fall of 3.2 points or -3.2 points.

Step-by-step explanation:

In integers , we use positive integers to show rise in amount whereas we use negative integers to show fall .

Given: A stock price rose 2.2 points in  Week 1.

i.e. +2.2 points rise.

The stock price fell 5.4  points in Week 2.

i.e. fall of -5.4.   (Much greater, than it rose)

The equation to represent the total  price change in stock would be

Total  price change = price rose in  Week 1 +  price fell  in Week 2.

= [+2.2 + (-5.4)] points

= 2.2 - 5.4 points   [ (+)(-) = (-)]

= -3.2 points

Hence, the total  price change in stock is fall of 3.2 points.

According to the question we have the following data:

the sum of 12 and x is -7

This problem can be resolved by formulating the following equation:

if the sum of 12 and x is -7 that means that:

Therefore, to calculate x we would have to make the following:

12 + x=-7

x=-7-12

x=-19

If x is -19 then if we substitue this value in the original equation we would find that the result is correct:

the sum of 12 and x is -7

12 +(-19)=-7

Ans: 3112mm^3

V = 1/3 base area x height

Base area is 23 x 23 = 529

(it's a square)

Find the diagonal of the base first & half it, giving you the mid-point of the square from bottom to the top of the shape or the vertex.

a^2 + b^2 = c^2

23^2 + 23^2 = c^2

Square root

C = root 23^2 + 23^2

Then, divide by 2 to get half of the length

root 23^2 + 23^2 / 2 = 23root2/2

Or

16.27 to 2d.p

Create a right-angle triangle & use Pythagoras Theorem again:

Dimensions of 16.27 (base) & 24mm (hypotenuse) given above. So, missing side/length is the height.

Rearrange equation: (a^2 + b^2 = c^2)

C^2 - b^2 = a^2

(doesn't matter where a & b is, it'll also give u the same answer)

24^2 - 16.27^2 = a^2

Square root

a = root 24^2 - 16.27^2

a = 17.65 to 2d.p

H=17.65 to 2d.p

V = 1/3 base area x height

= 1/3 x 529 x 17.65

= 3112.283333

= 3112.28 to 2d.p

(but, v=3112.170938mm^3 when I use exact value of the height)

Volume = 3112.17mm^3 to 2d.p

Or 3112mm^3 to 4 s.f. (as our integer)

(used exact value of numbers - in my calculation)

Hope this helps!

Step-by-step explanation:

To convert millimeters to centimeters we divide

As, 10 millimeters = 1 centimeter

So 1 centimeter = 1/10 millimeter

So here of we have 6 millimeters, so centimeters = 6/10 = 0.6cm

So the diameter of each bead in the necklace = 0.6cm

The diameter of bead in a necklaces is 0.6 centimeters.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

Given that, April is making necklaces using beads that are 6 millimeters in diameter.

We know that, both millimeters and centimeters is the unit to measure the length. One millimeter is equal to 0.1 centimeters and 1 cm is equal to 10 mm.

Here, 6 millimeters

= 6×0.1

= 0.6 centimeters

Therefore, the diameter of a bead is 0.6 centimeters.

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Answer: Convert the mixed numbers to improper fractions, then find the LCD and combine them.

Exact Form:

188

5

Decimal Form:

37.6

Mixed Number Form:

37

3

5

hope this helped have a nice day! :)

Answer:

Step-by-step explanation:

(124+64) /5

= 188/5

Answer is = 37.5

Answer: y = 1/8x+1

y=mx+b is slope intercept form

given m = 1/8 and a point we can find b by plugging in what we have

1=1/8(8)+b

1=1b

b=1

So then we know m = 1/8 and b = 1

y=1/8x+1 is the answer

Answer:

Option (3)

Step-by-step explanation:

Joe has a ruler which has markings for each millimeter, so the least measurement which Joe can do is in millimeter.

Since, 10 mm = 1 cm

Therefore, 1 mm = 0.1 cm

This rule states that Joe can measure a length or distance in nearest tenth of a cm only.

If length of a box = 13.67 cm,

So Joe can measure it as 13.7 cm approximately.

Therefore, Option (3) will be the answer.

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

Answer:

Area of ellipse=\(\pi ab\)

Step-by-step explanation:

We are given that

\(x=acos\theta\)

\(y=bsin\theta\)

\(0\leq\theta\leq 2\pi\)

We have to find the area enclose by it.

\(x/a=cos\theta, y/b=sin\theta\)

\(sin^2\theta+cos^2\theta=x^2/a^2+y^2/b^2\)

Using the formula

\(sin^2x+cos^2x=1\)

\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

This is the equation of ellipse.

Area of ellipse

=\(4\int_{0}^{a}\frac{b}{a}\sqrt{a^2-x^2}dx\)

When x=0,\(\theta=\pi/2\)

When x=a, \(\theta=0\)

Using the formula

Area of ellipse

=\(\frac{4b}{a}\int_{\pi/2}^{0}\sqrt{a^2-a^2cos^2\theta}(-asin\theta)d\theta\)

Area of ellipse=\(-4ba\int_{\pi/2}^{0}\sqrt{1-cos^2\theta}(sin\theta)d\theta\)

Area of ellipse=\(-4ba\int_{\pi/2}^{0} sin^2\theta d\theta\)

Area of ellipse=\(-2ba\int_{\pi/2}^{0}(2sin^2\theta)d\theta\)

Area of ellipse=\(-2ba\int_{\pi/2}^{0}(1-cos2\theta)d\theta\)

Using the formula

\(1-cos2\theta=2sin^2\theta\)

Area of ellipse=\(-2ba[\theta-1/2sin(2\theta)]^{0}_{\pi/2}\)

Area of ellipse\(=-2ba(-\pi/2-0)\)

Area of ellipse=\(\pi ab\)

She need a interest rate of 5.56%

Your wealth increases more quickly due to compound interest. Due to the fact that you will receive returns on both the money you invest and returns at the conclusion of each compounding period, it causes a sum of money to increase more quickly than with simple interest. As a result, you won't need to save as much money to achieve your objectives.

We are aware that A = P(1+rt), where A represents the Final Investment Value, is the simple interest formula.

P denotes the principal amount to be invested, r the interest rate, and t the number of time periods.

The formula for this issue is t = 18 Years, p = £90,000.

A = £9000 *2 => £18000\sr = ?

Fill in the appropriate values in the formula above to find 18000 = 9000(1+18r).

18r = 2 - 1\sr = 1/18\sr = 0.0555555556

Extend 0.0556

Ratio conversion: r = 0.0556 * 100 = 5.56%

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She need a interest rate of 5.56% .Your wealth increases more quickly due to compound interest.

Formula for Monthly Compound Interest. 12 times a year are used to calculate interest that is compounded monthly.

Formula for Quarterly Compounding. Four times a year are used to calculate interest that is compounded quarterly.

Formula for Daily Compound Interest.

Formula for Annual Compound Interest.

We are aware that A = P(1+rt), where A represents the Final Investment Value, is the simple interest formula.

P denotes the principal amount to be invested, r the interest rate, and t the number of time periods.

The formula for this issue is t = 18 Years, p = £90,000.

A = £9000 *2 => £18000\sr =

Fill in the appropriate values in the formula above to find 18000 = 9000(1+18r).

18r = 2 - 1\sr = 1/18\sr

= 0.0555555556

Extend 0.0556

Ratio conversion: r = 0.0556 * 100 = 5.56%

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